The purpose of this article is to assess whether correct application of robust estimators in construction of minimum variance portfolios’ (MVP) allows to achieve better investment results in comparison with portfolios defined using classical MLE estimators. Theoretical robust portfolios properties and portfolios investment effect are compared. This paper proposes a practical methodology of comparing alternative estimation methods, based on random portfolio selection. This approach enables to analyse investment effects of various portfolios. The empirical analysis shows that for MVP portfolios with nonnegative constraints created using robust methods, there is no significant risk improvement, and that even for most robust methods, there is an observable significant risk increase compared to the risk of classical portfolios. This paper also shows that robust portfolio estimators cause higher transaction cost.